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Math Help - differential equation equilibria!??

  1. #1
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    differential equation equilibria!??

    PLEASE HELP ME!!

    consider an interaction between two mutually inhibiting proteins with concentrations x and y, given by the differential equations:

    dx/dt = f(y)-x
    and
    dy/dt = g(x)-y

    where both f(y) and g(x) are decreasing functions.

    *show that equilibria occur when f[g(x)]=x

    how do i do the asterick part? any help would be very much appreciated..
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  2. #2
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    Quote Originally Posted by calcusucks View Post
    PLEASE HELP ME!!

    consider an interaction between two mutually inhibiting proteins with concentrations x and y, given by the differential equations:

    dx/dt = f(y)-x
    and
    dy/dt = g(x)-y

    where both f(y) and g(x) are decreasing functions.

    *show that equilibria occur when f[g(x)]=x

    how do i do the asterick part? any help would be very much appreciated..
    Require that both rates of change equal zero:

    f(y) - x = 0 => x = f(y) ..... (1)
    g(x) - y = 0 => y = g(x) .... (2)

    Solve equations (1) and (2) simultaneously:

    Substitute (2) into (1) ......
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